Pneumatic computing devices

ABSTRACT

A pneumatic computing device operating on the force balance principle to provide a desired ratio between input and output values of pressure or pneumatically to carry out multiplying, dividing and other mathematical functions. The device includes a force beam supported on a fulcrum, the beam being caused to swing in one direction by an input force element whose position along the beam relative to the fulcrum is adjustable to vary the effect of input pressure on the beam. Beam deflection is sensed by a detector included in a feedback loop producing an output pressure that is applied to a feedback force element tending to swing the beam in the reverse direction, the feedback force being such as to maintain the beam in equilibrium. The input and feedback force elements are both constituted by ball-and-cylinder elements exerting a force that depends on the ball area and on cylinder pressure.

United States Patent 11 1 Grier July 24, 1973 PNEUMATIC COMPUTING DEVICES Primary Eiaminer-Richard B. Wilkinson Assistant Examiner-Lawrence R. Franklin [75] Inventor. Davld G. Grier, Elklns Park, Pa. Atmmy Michael Eben [73] Assignee: Fischer & Porter Company,

Warminster, Pa.

57 ABSTRA T [22] Filed: Jan. 31, 1972 l C i A pneumatic computing device operating on the force [21] App! 222257 balance principle to provide a desired ratio between input and output values of pressure or pneumatically to [52] U.S. Cl. 235/200 WB, 91/359, 137/85 carry out multiplying, dividing and other mathematical [51] Int. Cl. G061! 1/06 functions. The device includes a force beam supported [58] Field of Search 235/200; 137/85; on a fulcrum, the beam being caused to swing in one 91/359; 92/129 direction by an input force element whose position along the beam relative to the fulcrum is adjustable to [56] References Cited vary the effect of input pressure on the beam. Beam de- UNITED STATES PATENTS flection is sensed by a detector included in a feedback 3,239,139 3/1966 Chapin et al. 235/200 WB Pmducmg mm)t pr'issure is aPPlied I 3,243 112 3/1966 Sorteberg 235/200 WB feedback element tendmg 2 the beam 2,991:006 7/1961 Clarke 235/200 WB the reverse direction. the feedback force being such as 3,072,326 1/1963 Rohmann et al. 235/200 WB to maintain the beam in equilibrium. The input and 3,159,343 12/1964 Hudson 235/200 WB feedback force elements are both constituted by ball- 3,l7l,33 0 3/1965 McCombs 137/85 X andqgylinde elements exerting a force that depends on the ball area and on cylinder pressure.

11 Claims, 12 Drawing Figures 6 km /Yoz /s She/#6 Senna as [864 1 LAP/:5

z, {res/ g 4 Sup/w I [l Pane/027m f five-wave. I8 I r Ann/FY1016 7 15 n flay 29 Q fi/Mmr) Fee-max EZEME/rr- B9 9 firmer/vs A? 4 0") a 7 /NP(J7' Ze-newr-fiote EFFw/m' 4264 A10) JAe/o's Gzasvevvr K2 new 5m Faceun firoragflezwec PNEUMATIC COMPUTING DEVICES BACKGROUND OF THE INVENTION This invention relates generally to pneumatic computing devices, and more particularly to pneumatic arrangements which operate on the force balance principlc and function as ratio devices, analog computers and adders or subtractors.

Pneumatically-operated force balance systems are well known, the system acting to algebraically combine torques created by one or more input signal pressures and spring forces to produce an output signal pressure that accurately represents a predetermined mathematical function of the input signals.

In a conventional pneumatic ratio device operating on the force balance principle, a force beam mounted on a fulcrum is caused to swing in the clockwise direction by a pneumatic input pressure applied to an input bellows coupled to the beam. Balancing of the beam is effected by a feedback loop including a detector acting to sense any slight beam deflection and coupled to a pneumatic relay to produce an output signal that is applied to a feedback bellows. The feedback bellows operates on the beam to produce a counterclockwise torque balancing the clockwise torque produced by the input bellows, causing the beam to return to its original equilibrium state.

The ratio between the input and output signals may be varied by shifting the position at which the input bellows engages the beam. The effect of bellows expansion in response to an applied pressure is expressed by the axial deflection of the bellows from its free length. If a shift in the position of the input bellows along the beam also displaces the axial position of the bellows relative to the beam, this change in the axial position introduces an error. The error is caused by a force change on the beam which is equal to the product of the bellows spring gradient and the axial deflection. While it is possible to align the ratio device to avoid this error, the need for alignment adds to the cost of the instrument.

The spring gradient of the bellows also causes another source of error. When the input bellows of a ratio device is near the fulcrum of the force beam, its stiffness or gradient is not significant, but when the bellows is shifted to a point well displaced from the fulcrum, the overall gradient of the beam is much higher and therefore less sensitive, particularly since the gradient of the bellows as felt by the beam is proportional to the square of the distance from the fulcrum. Inasmuch as the sensitivity of a ratio device undergoes a large change as the bellows is shifted along the beam and beam sensitivity is directly related to the accuracy of the device, the performance of the device becomes progressively poorer as the bellows is shifted away from the fulcrum.

Similar drawbacks are encountered in pneumatic computers in which input pressures are applied to a force beam by bellows whose positions along the beam are adjustable.

SUMMARY OF THE INVENTION In view of the foregoing, it is the main object of this invention to provide highly accurate and low cost pneumatic computing devices of simple design operating on the force balance principle.

More specifically, it is an object of this invention to provide a penumatic computing device of the above type in which the force members are in the form of balland-cylinder elements rather than bellows, whereby the elements may be shifted along the associated beam without appreciable friction.

. A significant advantage of the invention resides in the fact that the zero gradient of the ball obviates the need for critical alignment of the force element and of the beam on which it operates.

Also an object of the invention is to provide a pneumatic ratio device in which input pressure is applied to the beam by a ball-and-cylinder force element and in which a similar element is used to apply a feedback force to the beam to maintain beam equilibrium.

Yet another object of the invention is to provide a pneumatic computer operating on the force beam principle and employing ball-and-cylinder input and feedback force elements to carry out multiplying, dividing, squaring and square root functions.

Briefly stated, these objects are attained in a force balance arrangement in which a force beam supported on a fulcrum is caused to swing in one direction by an input force element whose position along the beam relative to the fulcrum is adjustable to vary the effect of input pressure on the beam. A flapper-nozzle detector serves to sense beam deflection, the detector being coupled to a pneumatic relay producing an output pressure which is applied to a feedback force element tending to swing the beam in the reverse direction, the feedback force being such as to maintain the beam in equilibrium. The force elements may both be constituted by ball-and-cylinder elements whose balls exert a force on the beam which depends on the ball area and on cylinder pressure.

OUTLINE OF THE DRAWINGS For a better understanding of the invention, as well as other objects and features thereof, reference is made to the following detailed description to be read in conjunction with the accompanying drawings wherein:

FIG. 1 is a schematic diagram of a known form of pneumatic ratio device;

FIG. 2 is a schematic diagram of a ratio device in accordance with the invention;

FIG. 3 is a perspective view of a preferred embodiment of a ratio device in accordance with the invention, including a pivoted arm to adjust the position of the input force element along the force beam;

FIG. 4 is a schematic diagram of the arrangement shown in FIG. 3;

FIG. 5 is a simplified schematic diagram of the arrangement shown in FIG. 3;

FIG. 6 separately illustrates the action of the pivoted lever of the FIG. 3 device;

FIG. 7 separately illustrates the action of the spring of the FIG. 3 device;

FIG. 8 is a perspective view of a pneumatic analog computer in accordance with the invention operating in the multiplying mode;

FIG. 9 is a schematic diagram of the multiplier shown in FIG. 8;

FIG. 10 is a schematic diagram of the analog computer operating in the dividing mode;

FIG. 11 is a schematic diagram of an addersubtractor in accordance with the invention; and

FIG. 12 is a sectional view of a ball and cylinder pressure element in accordance with the invention.

DESCRIPTION OF THE INVENTION RATIO DEVICES:

Referring now to FIG. 1, there is illustrated a simple pneumatic ratio device. The purpose of this figure is to explain the deficiencies resulting from the conventional practice in which bellows are used to apply input and rebalancing forces maintaining beam equilibrium.

Force balance beam is supported on a fulcrum 11 and is caused to swing in a clockwise direction by a pneumatic input pressure P applied to an input bellows 12. This bellows is slidable along a surface 13 parallel to beam 10. The active end of bellows 12 is provided with a roller 14 which engages the beam at a point to the left of fulcrum 11. The distance between this point and fulcrum 11 is represented by symbol x.

Balancing of beam 10 is effected by a feedback loop including a flapper-nozzle detector 15 operatively coupled to the beam adjacent the right extremity thereof to sense any slight beam deflection. Detector 15 is coupled to pneumatic relay l6, producing an output signal P which depends on the flapper position relative to the fixed nozzle.

Output signal P is applied to a feedback bellows l7 operatively coupled to the beam at a fixed point to the right of the fulcrum and spaced therefrom by a distance a. The zero position of the beam is maintained by a spring 18 coupled between the right end thereof and ground.

Output signal P applied to feedback bellows 17 produces a counterclockwise torque that balances the clockwise torque produced by input bellows l7, causing beam 10 to return to its equilbrium state. In this state, the pressure applied by the input bellows multiplied by distance x" is equal to the pressure applied by the feedback bellows multiplied by distance a."

The ratio between input and output signals P and P may be varied by shifting the position of input bellows 12 along the beam, thereby changing the value of distance x." When the point at which the input force is applied to the beam is very close to its fulcrum, the mechanical advantage of the lever is very low; hence a large change input signal I produces a very small change in output signal P But if this point is shifted away from the fulcrum so that it is near the left end of the beam, the mechanical advantage is much greater, whereby a small change in input signal produces a very large change in the output signal.

In the foregoing analysis, ideal conditions have been assumed. But in practice, when using bellows, these conditions do not prevail. In fact, certain drawbacks are encountered which render the standard ratio device somewhat unreliable and inaccurate.

For example, if sliding surface 13 on which input bellows 12 is shifted is not perfectly parallel to beam 10, then the value (e) representing the axial deflection of input bellows 12 from its free length will be altered as the bellows is shifted to different positions along the beam.

Value (e) is a factor in the following force-balance equation:

P A X K, ex P 14 a k bf where:

A, is the effective area, in square inches, of input bellows 12, K, is the spring gradient of the bellows in pounds per inch, and f is the deflection of zero spring 17 from its free length. Hence:

A x (P k ex/Apr) A a (P K bf/A a) If K,ex/A,x) is made equal to 3 and K bflA a is made equal to 3 Thence:

A11(P1 2 (P23) n 2 (P1 (P2 R (P 3) (P 3); where R A x/A a Value (e) is therefore inportant, for it establishes the bias signal that normally is required for a pneumatic signal. In practice, most pneumatic signals are based on a 3 to 15 psi range. Before proceeding with pneumatic computation, one must therefore substract three. Hence, we are really looking for a 0-12 psi input range rather than a 3-15 psi signal which is received by the instrument. Accordingly, one is required to provide some adjustment that will enable the sliding surface for the input bellows to be made parallel during the assembly and testing of the device.

Also highly significant is value K the spring gradient of the bellows. In order to maintain a constant spring gradient regardless of temperature, a special alloy material is required for the bellows. While such special metals are commercially available, they are quite expensive and add materially to the cost of the instrument.

To operate effectively, a ratio device functioning on the force-balance principle must be made sensitive to small changes in input pressure. When the slidable input bellows 12 is located near fulcrum 11, the effect of the stiffness or gradient of this bellows on the beam is not appreciable.

But when input bellows 12 is shifted to a point adjacent the outer end of the beam, the overall gradient of the beam is much higher and therefore less sensitive. Actually, the gradient of the bellows as felt by the beam is proportional to the square of the distance from the fulcrum.

As a consequence, the sensitivity of the device changes markedly as the bellows is shifted along the beam. The sensitivity of the beam or the radient of the beam is directly related to the accuracy of the ratio device. As the beam becomes stiffer, or with a higher total gradient, the performance of the device becomes much poorer. If on the other hand the beam is excessively sensitive, the device is rendered penumatically unstable, thereby producing an oscillating output signal. Thus, with an input bellows associated with the beam and sliding therealong, we have in effect a moving spring gradient. The system therefore suffers from the influence of changes in the system gradient.

Referring now to FIG. 2, there is shown a pneumatic ratio device according to the invention. In place of the input and feedback bellows included in the ratio device shown in FIG. 1, the invention makes use of an input ball-and-cylinder force element 19 and a feedback balland-cylinder force element 20.

Ball and cylinder input element is shiftable in a straight line along surface 13 parallel to the beam, the ball engaging the beam surface. To maintain this straight line, the input element may be made to move within a suitable groove or a guide rod may be provided.

input element 19 is connected by a bracket 21 to one end of a bias spring 22 whose outer end is secured to a lateral extension 23 on beam on the feedback side of the beam, the spring being parallel to the beam. Hence, as input element 19 is shifted away from fulcrum ll, bias spring 22 is stretched accordingly.

In a ball-and-cylinder element, the force generated by the ball located at one end of the cylinder is strictly a function of the pressure within the cylinder acting on the area of the ball. In the case of input element 19, the pressure applied to the ball thereof is that produced by input signal P,, while in the case of feedback element 20, it is that produced by output signal P If the ball of the force element were to move slightly along the axis of the cylinder, no perceptible change in force would occur. Thus, the parallelism of the beam and the guiding surface for the input element is not critical and, unlike the bellows arrangement shown in FIG. 1, no adjustment is required to assure parallelism.

An increase or decrease in ambient temperature gives rise to a minute expansion or contraction of the ball which has no measurable effect on the accuracy of the system. Moreover, the ball has no stiffness or gradient of its own; hence movement of the ball along the beam has no influence whatever on the overall stiffness or gradient of the beam. Thus as contrasted to a bellows arrangement, the sensitivity of a ratio device using ball-and-cylinder force elements remains constant regardless of the position of the ball along the beam.

The simple rolling motion of the ball along the surface of the beam presents no difficulty. With a sliding bellows however, a ball or low friction bearing is required to attain the same advantage.

In a ratio device as shown in H0. 2 in accordance with the invention, the desired final formula is:

where P, is input pressure P is output pressure R is the ratio Values P, and P are 3 to psi signals representing 0 to 100 percent full scale. One must therefore subtract 3 psi to obtain true 0 percent signals. In the final formula for ratio R, we must therefore subtract 3 psi for both P, and P We will now show how the final formula is derived.

The equation for summing forces and lever arm lengths (torques) on the beam is:

f deflection of zero spring from free length e deflection of bias spring from free length Reworking above:

(K lx/A,x) is made equal to 3 and (K,bf/A a) (K lelA a) is made equal to 3 Then:

R (P, 3) (P 3) where R =A,I/A a which is desired final formula. i [t is interesting to note that it is possible to eliminate the zero spring K,. The length of spring K would then be adjusted. The formula is then as follows: i

P, A, x K (e+x) P A a Reworking P, A, x K lx P, A: a K le A,x (P, K lxlA, x) A a (P K le/A a) (K,Ix/A,x) and (K le/A a) are made equal to 3 then R (P, 3) (P 3) which is desired final formula.

In FIG. 2, the input force element has its ball moving in a straight line along beam 10. Though straight line motion is the simplest, from the mathematical point of view, mechanical movement along an arc is easier to accomplish in a practical embodiment. This is the arrangement shown in FIGS. 3, 4 and 5 wherein input ball-and-cylinder element 19 is mounted at the end of a ratio pointer 24 pivoted on a post 25.

The pointer acts as a lever, whereby when the pointer is shifted along an arcuate ratio-indicating scale, the ball of the input ball-and-cylinder element 19 swings on an arc on force beam 10. FIG. 6 shows in..plan view the arc through which the input element 19 and the end of spring 22 travel as angle T is changed.

The formula will now be given in simplified form. Basic formula:

P,, A,a k al F e P,,,,, A x Where F, is force exerted by zero spring (K this reduces to r 2 in 31 2 r aul B l 2 which can be made as shown previously to be- R (P,, 3) (P 3) where R A,a/A-,x manually set ratio Since the standard pneumatic signal is 3 to 15 psi, the (P,,, 3) and aul 3) corrects for the biased signal (3 psi represents 0 percent full scale). A more accurate derivation is as follows: Summing forces as before:

P, A,xk [F+Dsin (T)e]l=P,A,-K, bf This is the effective force caused by the spring. Derived in next section. Since I D sin (1') Then:

P, A, D sin (T) k, [F+D sin (T)e]L P, A,a K,

f P, A, D sin (T) k,D sin (T)! P,A,a K,bf+

(Fe)k,l A,D sin (T) (P, k D sin (T)I/A,Dsin (T))=A,a (P, f 1 f 2l/Az l (k,l/A,) is made equal to 3 and (K,bf+ (Fe)k l/A,a) is made equal to 3 Then A,D sin (T) (P, 3) A 0 (P, 3)

A,D sin (T)/A a (P, 3) (P 3) which is R (P, 3) (P 3) where R A,D sin (T)/A a which is the desired final formula. Because the spring also moves through an are, this requires compensation which, fortunately, is easily obtained.

FIG. 7 schematically shows how the spring 22 moves through an arc during changes in the ratio pointer 24. The derivation of the spring will now be explained. Spring length equal to ([F+D sin (T)] [D-D cos )l and cos a F+D sin (T)/([F+D sin (T)] l- [D-D cos nz 1/2 The effective force caused by the spring on the beam is equal to the spring length multiplied by cos a (vector angle). Therefore:

EFF FORCE (SPRING LENGTH) (cos a) F+D sin (T) which is the quantity used in the original derivation.

Pneumatic Analog Computers. Pneumatic computers are known for solving simple arithmetic functions. Computations such as those involved in stock blending, flow proportioning and mass flow computing may be accomplished in an arrangement which accepts one or two 3 to 15 psi input signals and transmits a 3 to 15 psi output signal proportional to the product or to the quotient of the two inputs, or to the square or square root of one input.

These input pressures are applied by means of bellows to a force arm whose deflection is sensed by a flapper nozzle detector to produce in a pneumatic relay, an output signal which is fed to a feedback bellows to produce a restoring force on the force arm maintaining the system in equilibrium.

Commercially available pneumatic computers of the above-described type suffer from drawbacks similar to those experienced with ratio devices using input and feedback bellows, as previously described.

In a pneumatic computer in accordance with the invention as shown in FIG. 8, the arrangement is essentially the same as in the ratio device shown in FIG. 3. That is to say, the movable input force element 19 is a ball-and-cylinder element mounted at the end ofa lever 24' pivoted on a post 25, and the feedback force element 20 may also be a ball-and-cylinder element. However, instead of a manually adjustable pointer for shifting the position of the input force element in an are along feedback beam 10, this shift is effected pneumatically by a capsule 30 or any other suitable form of pressuresensitive transducer operatively coupled to lever 24 to adjust the position of input element 19 as a function of a second input pressure P FIG. 9 shows the pneumatic computer in schematic form, the two input pressures P, and P being applied to the ball-and-cylinder force element 19, and the capsule 30 respectively, and the output pressure P, being taken from pneumatic relay 16. For the manually set pneumatic ratio device, the basic formula is:

With the addition of capsule 30 to pneumatically adjust the ratio, the value of R is made equal to (P 3)/l2. The new formula which expresses the multiplying action of the pneumatic computer is:

As in the ratio device, all signals are 3-l5 psi and must have 3 psi subtracted from the signals for proper performance.

In the squaring mode, the unit is the same as in multiplying except that a single input P, is applied to both input elements 19 and 30.

Therefore:

In the dividing mode, the computer unit is similar to the multiplier shown in FIG. 9, but nozzle 15 the of detector is moved to the opposite side of force beam 10 and the feedback element 20 is attached to the movable lever 24' whose position is controlled by capsule 30.

In this dividing arrangement, the pneumatic pressure P, is taken as an output from pneumatic relay 16, whereas the input pressure P is applied to input element l9 and the input pressure P to input element 20. Thus:

To carry out square root computations, the arrangement is the same as in the divider set-up shown in FIG. 10, but in this instance the output signal from pneumatic relay 16 is also applied to capsule 30. Thus:

Thus, in a pneumatic computer in accordance with the invention, a pressure-responsive capsule is added to the ratio device, which capsule serves to change the position of the lever carrying the input force element to cause this element to shift its position along the force beam.

The multiplying capability comes from pneumatically shifting this lever in accordance with input pressure P;, while applying input pressure P, to the input force element. Consequently, we have two factors-a length and a force-both of which are variable. The product of these factors, when rebalanced by the feedback mechanism, causes the device to carry out a multiplying function.

To cause the instrument to carry out functions other than multiplying, an additional detector nozzle is provided on the opposite side of the force beam. By changing from one nozzle to the other or changing the feedback or output pressure from one element to another, it becomes possible to accurately handle the functions of multiplying, squaring, dividing and extracting the square root of pneumatic signals in a single inexpensive instrument.

While in the computer arrangement, movement of the input element along the beam is shown in the figures as being along an arc, in practice an arrangement providing straight line motion may be used in lieu of that shown. The are method is simpler to carry out. The angle of the arc, since a trigonometric sine function is involved, must be kept small to minimize the effect of this non-linearity. However, either the straight-line or are method of moving the ball-and cylinder element along the force beam affords satisfactory performance.

If one were to use a bellows instead of a ball-and cylinder force element, particularly for the element moving along the beam, the problems which arise from the use of bellows in ratio devices become even more critical in a pneumatic computer. It would be extremely difficult, should one use a simple capsule for this purpose, to accurately shift the position of a bellows along the beam, whereas the free movement of a ball-andcylinder force element presents no difficulty in this regard.

Also, the sensitivity of stiffness problem encountered in bellows actuated devices, as noted previously, becomes very critical in a pneumatic computer which must operate over a wide range of motions. The pneumatic stability of the instrument would be very difficult to maintain if there were a gradient on the moving input element, as in the case when using bellows. But in a pneumatic computer incorporating ball-andcylinder force elements, the position of the ball has no effect on the apparent stiffness of the force beam. Thus, with a pneumatic computer in accordance with the invention, a constant beam sensitivity is maintained, thereby improving the accuracy of the instrument.

Adders and Subtractors. Pneumatic adders and subtractors are available commercially, the devices being adapted to effect summation or subtraction of two or more input signals. These are used industrially, for example, to totalize a number of flow loops to obtain the total flow from a multiple flow system. They usually employ a force-balance system operating in conjunction with bellows to produce a single modified output pressure.

Referring now to FIG. 11, there is shown a pneumatic adder-subtractor in accordance with the invention and including a force beam 10 supported in a fulcrum 11, the position thereof being sensed by a flapper-nozzle detector coupled to a pneumatic relay 16 to provide an output pressure P In this arrangement, input pressure P, and P are applied to one end of the beam by ball-and-cylinder force elements 31 and 32 engaging the beam on opposite sides thereof at fixed locations. The output pressure P, is applied to the feedback ball-and-cylinder force element disposed at the other end of the beam on the upper side thereof, the lower side having a ball-andcylinder force element 33 to which an input pressure P, is applied. Elements 20 and 33 are all at fixed positions. In this arrangement:

P, P, P P (basic formula).

In the above equations, all elements have the same area A, at fixed locations.

For biased signals, the following equation applies:

(P1"'3)+ r a r If one of the input signals is omitted, then the biasing must be considered. For example:

( rr r- This is not equal to P, P, P,. Therefore, to make the unit more versatile, a bias spring K which is made adjustable to handle various input situations, is added to beam 10. The fi'nal formula is:

THE BALL AND CYLINDER ELEMENT Referring now to H0. 12, there is shown a preferred form of ball-and-cylinder element comprising a cylindrical housing 35 having an upper head portion 36 provided with a circular groove 36A adapted to receive a snap ring for mounting the element. In practice, head 36 may be threaded for mounting purposes. The housing is provided with a lateral opening 37 and a fitting 38 for pressure connection.

Received within the main hole 39 is the ball 40, the diameter of the hole being closely controlled to avoid pressure leakage.

As pointed out previously, the ball-and-cylinder element is most advantageous when this element is movable relative to the beam. However, in those instances where the pressure-responsive element is fixedly mounted, one need not use a ball-and-cylinder element and one may use other known forms of pressureresponsive elements, such as bellows.

While there have been shown and described, preferred embodiments of pneumatic computing devices in accordance with the invention, it will be appreciated that many changes and modifications may be made therein without, however, departing from the essential spirit of the invention.

1 claim:

1. A pneumatic computing device comprising:

a. a force beam supported on a fulcrum;

b. a pressure-responsive input force element engaging said beam;

c. means to apply a first input pressure to said input element whereby an input torque is produced tending to swing said beam in one direction, the magnitude of the input torque depending on said input pressure, input element area and the distance between the input element and the fulcrum;

d. a detector operatively coupled to said beam to sense any deflection thereof;

e. means responsive to said detector to produce an output pressure;

f. a pressure-responsive feedback element responsive to said output pressure and engaging said beam to produce a torque in the reverse direction to an extent counteracting said input torque to maintain said beam in equilibrium, said feedback torque having a magnitude depending on output pressure, feedback element area and the distance between said feedback element and the fulcrum; and

. means to shift one of said elements along the beam relative to said fulcrum to vary the distance there between, the shiftable element being a ball and cylinder element whose ball engages said beam, said ball and cylinder element being constituted by a cylinder having a circular hole forming a socket for the ball, the diameter of the hole substantially matching the diameter of the ball to avoid pressure leakage, and a duct communicating with said hole to apnly a pneumatic pressure thereto whereby the fOI'Ct. znerated by the ball is strictly a function of the pressure within the cylinder acting on the area of the ball.

2. A device as set forth in claim 1, acting as a divider, said shifting means being coupled to said feedback element, and being responsive to a second input pressure causing said feedback element to assume a position depending thereon;

3. A device as set forth in claim 1, acting as a ratio device, wherein said shifting means is manually operated to vary the position of the input element; thereby to adjust the ratio between the input and output pressures.

4. A device as set forth in claim 1 acting as a multiplier, said means shifting said input force element including a pressure-sensitive transducer responsive to a second input pressure whereby said output pressure is the product of the input pressure applied to said input element and the input pressure supplied to said transducer.

5. A device as set forth in claim 4, further including a span spring extending between said arm and a point on said beam adjacent said feedback element.

6. A device as set forth in claim 1, further including spring means biasing said beam.

7. A device as set forth in claim 6, wherein said manually-operated means is constituted by a pivoted pointer arm operating along a ratio-indicating scale.

8. A device as set forth in claim 7, wherein said second input pressure is the same as the first input pressure whereby the output pressure is the square of the input pressure.

9. A device as set forth in claim 7, wherein said transducer is a capsule secured to one end of a pivoted arm, the other end of which is attached to said input element. 1

10. A device as set forth in claim 9, further including a zero spring extending between ground and said beam at a point adjacent said input element.

11. A device as set forth in claim 10, wherein said input pressure is the same as said output pressure, whereby the output pressure is then the square root of the first input pressure.

Inventor(s) I Um ?m STA ES {HEM OFFICE- 4 C'EBTEFICATE OF CGRREQTION- 4 3 748 454 Dated July 24 ,il973 Patent No.

David G, Grier It is certifiedrhat error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

'Col. 4, line 5, "K ex/A .x) is" should have read K ex A 'x is --1 (without parenthesis line 10,: "A eho uld have I e ad A 'i'i Col. 6-, linel "i It" should have read- It v line "38 :';'(P, 31" shouldyhav'e read (P i i z", 1 '3 should have read (-T),] l Col 8, line 37 -3) S ou have read? g- Col. 10, 'line 7. -"P vA ,x A x" should have read i P A x P 14 x Signeiand sealed this 1stv day of January 1974,

( A Attes't EDWARD M FLETCHER-,JR. RENE D. TEGTMEYER Attesting Oificerg H i Acfcing Cemmissioner .o f Patehts v -UN1EED STATES iATENT OFFICE CEBTiE-ICATE OF CORRECTION Patent 3,748,454 Dated y 2 1913 Invenmfls) David G. Grier It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

Col. 4, line 5, "K ex/A x) 'is" should have read M K ex A 'x is (without parenthesis) line 10, "A s" should have read A x Col. 6, line 1 "i It" should have read It line 38 (P 31" should have read (P 9 l' line 7 1 should have read (T)] Colfi 8, line 37 (1 -3) should have read (P2-3) /2 Col. 10, line ,7, :"P A x A x" should have read P:L A X P4 A X Signed and sealed this 1st day of January 1974.

Attest 2 EDWARD M.FLETCHER,JR. RENE D. TEGTMEYER Attesting Officer Acting Commissioner of Patents 

1. A pneumatic computing device comprising: a. a force beam supported on a fulcrum; b. a pressure-responsive input force element engaging said beam; c. means to apply a first input pressure to said input element whereby an input torque is produced tending to swing said beam in one direction, the magnitude of the input torque depending on said input pressure, input element area and the distance between the input element and the fulcrum; d. a detector operatively coupled to said beam to sense any deflection thereof; e. means responsive to said detector to produce an output pressure; f. a pressure-responsive feedback element responsive to said output pressure and engaging said beam to produce a torque in the reverse direction to an extent counteracting said input torque to maintain said beam in equilibrium, said feedback torque having a magnitude depending on output pressure, feedback element area and the distance between said feedback element and the fulcrum; and g. means to shift one of said elements along the beam relative to said fulcrum to vary the distance therebetween, the shiftable element being a ball and cylinder element whose ball engages said beam, said ball and cylinder element being constituted by a cylinder having a circular hole forming a socket for the ball, the diameter of the hole substantially matching the diameter of the ball to avoid pressure leakage, and a duct communicating with said hole to apply a pneumatic pressure thereto whereby the force generated by the ball is strictly a function of the pressure within the cylinder acting on the area of the ball.
 2. A device as set forth in claim 1, acting as a divider, said shifting means being coupled to said feedback element, and being responsive to a second input pressure causing said feedback element to assume a position depending thereon.
 3. A device as set forth in claim 1, acting as a ratio device, wherein said shifting means is manually operated to vary the position of the input element; thereby to adjust the ratio between the input and output pressures.
 4. A device as set forth in claim 1 acting as a multiplier, said means shifting said input force element including a pressure-sensitive transducer responsive to a second input pressure whereby said output pressure is the product of the input pressure applied to said input element and the input pressure supplied to said transducer.
 5. A device as set forth in claim 4, further including a span spring extending between said arm and a point on said beam adjacent said feedback element.
 6. A device as set forth in claim 1, further including spring means biasing said beam.
 7. A device as set forth in claim 6, wherein said manually-operated means is constituted by a pivoted pointer arm operating along a ratio-indicating scale.
 8. A device as set forth in claim 7, wherein said second input pressure is the same as the first input pressure whereby the output pressure is the square of the input pressure.
 9. A device as set forth in claim 7, wherein said transducer is a capsule secured to one end of a pivoted arm, the other end of which is attached to said input element.
 10. A device as set forth in claim 9, further including a zero spring extending between ground and said beam at a point adjacent said input element.
 11. A device as set forth in claim 10, wherein said input pressure is the same as said output pressure, whereby the output pressure is then the square root of the first input pressure. 